In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500.
The number of students who like their core branches is
Answer
(A)
Explanation
Students who like at least one of the two: \(10000 - 1500 = 8500\).
Let \(c\) students like their core branches, so \(4c\) like other branches. The 500 who like both are counted in both groups, so they are subtracted once:
\[c + 4c - 500 = 8500 \implies 5c = 9000 \implies c = 1800.\]
Check: 7,200 like other branches, and \(1800 + 7200 - 500 = 8500\). Adding the 500 instead, as if those students formed a separate group, gives \(5c = 8000\), that is 1,600 (option C).
Answer: A